Let R 2 have the inner product of Example 1. Show that the CauchySchwarz inequality holds for
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Let R2 have the inner product of Example 1. Show that the Cauchy–Schwarz inequality holds for x = .(3,– 4) and y = (–4; 3).
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EXAMPLE 1 Fix any two positive numbers-say, 4 and 5-and for vectors u = (₁, ₂) and v = (v₁, v₂) in R², set (u, v) = 4u1v₁ + 5u2v2 Show that equation (1) defines an inner product. (1)
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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